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A363896
Numbers k such that the sum of primes dividing k (with repetition) is equal to Euler's totient function of k.
0
9, 15, 16, 42
OFFSET
1,1
COMMENTS
No more terms less than 1.6*10^7.
FORMULA
{k : A001414(k) = A000010(k)}.
MATHEMATICA
Select[Range[2, 1000], EulerPhi[#] == Plus @@ Times @@@ FactorInteger[#] &] (* Amiram Eldar, Jun 27 2023 *)
PROG
(Python)
from sympy import factorint, totient
A001414 = lambda k: sum(p*e for p, e in factorint(k).items())
def g():
k = 2
while True:
if A001414(k) == totient(k): yield(k)
k += 1
for a_n in g():
print(a_n)
(PARI) is(k) = my(f=factor(k)); f[, 1]~*f[, 2] == eulerphi(f); \\ Amiram Eldar, Jun 27 2023
CROSSREFS
Subsequence of A257048.
Other sequences requiring a specific relationship between A000010(k) and A001414(k): A173327, A237798, A280936.
Sequence in context: A324879 A066942 A257048 * A061838 A037002 A071149
KEYWORD
nonn,more
AUTHOR
Darío Clavijo, Jun 26 2023
STATUS
approved